Zoom International Math League: Estimation Challenge Part 1 (Weekly Brain Potion Discussion)

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Estimation Challenge Part 1 (Weekly Brain Potion Discussion)

Those of you who have taken a class with me (Mr. John) would recognize my trusty coffee mug that often appears in the class videos.

As it is important to stay hydrated, I also have a bottle of water with me at my desk most of the day. The bottle is pictured below, filled to the top with water, next to a ruler for a sense of scale. (Click on the image to download a full size version.)

Your challenge this week is to guess the weight of the bottle filled with water in grams.

Share your answer and reasoning below and we'll announce the person who got closest to the actual weight next Friday when we launch part 2 of the estimation challenge.

I think the weight of the bottle filled with water is 340g.

I see the bottle as a cylinder with a cone. I think the weight of the bottle itself is 5g. Then I think the weight may be 340g.

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I looked at it like a cylinder with an cone on top

With a height of around 16cm for the cylinder, and a base radius of around 6cm, plus a cone with height of 8cm and a base radius of 6cm, you end up with A=16*5^2*pi+1/3*8*5^2*pi,you get 466 2/3pi cubic centimeters, which is around 1466 cubic centimeters. Since 1 cubic centimeter is a milliliter of water, which is 1 gram of water, I got a final weight of 1466g of water. Due to the weight of the bottle, of which the average weight of a similar sized bottle is around 20g, I would estimate that the final weight of the bottle is 1486g

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Great job to Christoper this week, who was $12$ grams away from the actual answer!

The idea of thinking of the bottle as a cylinder and a cone was a good one. In fact the volume of the full bottle (measured by pouring the bottle out) was around $1400$ mL. It is correct to say $1$ mL of water weighs approximately $1$ gram, so the water inside the bottle weighted about $1400$ grams. The bottle itself was a little heavier than Christopher estimated, weighing in at roughly $75$ grams.

The actual weight was $1474$ grams as seen in the attached image below:

Bottle Weight of 1474 grams

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